Honestly, I don't see how Gingrich's Tiffany's credit-line is of any relevance. If Obama's proven anything, it's that he's an utterly inept politician who allows those "entrenched" insiders to make his every decision for him, whether it be about the economy or the wars. There are two areas, at least, where I think Gingrich could do better than Obama:
1.) Making his own decisions: Obama's proven again and again that he's just not capable of challenging economists, generals, and other advisers on domestic and foreign issues. Gingrich, however, has been around longer than most, and he probably would do a lot better job at cutting through the bullshit to press his own objectives (does Obama even have personal objectives anymore, or is it just his aids and advisers running the show like W.'s did?). Gingrich's sense of arrogance would probably make him harder to push around then Obama, who in contrast likes to think of himself as being "above the debate" but is actually the guy getting trampled by it.
2.) Leveling with the American people: This is one area where Obama has been beyond horrendous. American people don't understand what he's doing, and since he's so terrible at explaining it to them conservatives easily taint the discussion at the earliest stage, just like they did with Obamacare. Sure, he's got a good vocabulary, but that's not worth anything if you can't make a compelling case for anything you're doing in office. Obama may have seemed like a good debater 3 years ago, but that was when he was up against McCain and Palin, neither of whom are capable of making coherent statements. Gingrich, by comparison, is a much more competent orator than anyone in the running now, and one who seems to do a better job of sounding smart while breaking ideas down to a level normal people can understand.